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The difference between the speed along and against the river is 8 km/h and the time taken to cover a journey from initial to final point and return to initial point is 3 hr. What is speed along with the river if the distance between the initial and final Point is 9 km?

The difference between the speed along and against the river is 8 km/h and the time taken to cover a journey from initial to final point and return to initial point is 3 hr. What is speed along with the river if the distance between the initial and final Point is 9 km? Correct Answer 12 km/hr

Let the speed of the boat in still water be x and speed of stream be y

Speed along with river = (x + y) km/h

Speed against with river = (x - y) km/h

According to the question,

x + y - x + y = 8 km/h

⇒ 2y = 8

⇒ y = 4 km/hr

Also,

Total time taken, 9/(x + 4) + 9/(x - 4) = 3

⇒ 6x = x2 - 9x

⇒ x2 - 6x - 16 = 0

⇒ (x - 8) (y + 2) = 0

⇒ x = 8

∴ Speed in downstream = x + y = 8 + 4 = 12 km/hr

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